Microwave measurement system for piston displacement

ABSTRACT

A microwave measurement system is utilized for the determination of displacement of a piston in a fluid filled cylindrical structure. The piston plus cylindrical encasement of the hydraulic system is modeled as a uniform cylindrical waveguide terminated in a metal plate. A novel shaped probe antenna to measure the slope of the relative phase of the reflected equivalent voltage wave with respect to frequency. The idea to measure the slope of the relative phase is novel and requires a new antenna structure. Instead of using the phase slope with respect to frequency, the total phase shift in a given frequency range is used to determine the location of the piston in the cylindrical chamber. Simulation and measurement will be used to determine the impedance of the antenna as well as the electromagnetic field at different locations inside the cylinder. In addition, the antenna will be analyzed to optimize its design, which ought to result in minimizing the reflections.

RELATED APPLICATION

This application is a continuation application of allowed U.S.application Ser. No. 10/794,426, filed on Mar. 5, 2004 Pat. No.7,098,671 issued on Aug. 29, 2006, which in turn claims the benefit ofpriority from U.S. Provisional Patent Application No. 60/453,082, filedon Mar. 7, 2003, the entirety of which are incorporated herein byreference.

BACKGROUND

Hydraulic systems are typically used to provide strong forces found inheavy-duty machinery. Hydraulic systems are found in heavy constructionequipment, such as, cranes, bulldozers, excavators, dump trucks,forklifts, graders, as well as in large agricultural machinery, such as,tractors, combines, etc. The hydraulic/pneumatic systems currently usedsuffer from a lack of precision in control. Electric motors are oftensubstituted for hydraulic/pneumatic systems in light duty machinery toaccomplish precision control. Examples of precision control usingelectric motors include robots that are used in automobile manufacturingand in circuit board assembly industries. Such robots havesub-millimeter precision and are useful for light-duty applications.Heavy machinery applications typically mandate the use of hydraulicsystems; however, exact control usually cannot be achieved.

Leakage of hydraulic/pneumatic fluid from one side of a piston to theother side results in undesirable movement in machinery, for example, inattempting to steady the position of a fire engine ladder or of a craneduring installation of steel beams. A feedback control system inconjunction with an apparatus that senses a piston position couldcorrect the slippage of hydraulic/pneumatic pistons.

SUMMARY

A technique that can provide accurate location of a piston is developed.It uses microwave propagation in hydraulic or pneumatic cylinders. Sucha method and apparatus could be used as a sensing system to providehighly accurate position feedback information for hydraulic/pneumaticcontrol system.

A computer controlled system using an accurate sensing device (sensor)in hydraulic/pneumatic cylinders is currently not available but isneeded to automate heavy machinery. Instead of the movement of severaldifferent control valves, an operator will benefit from a moreconvenient man machine interface, such as a mouse, touch screen, touchpad, joystick or a keypad for numerical entry. Simultaneous activationof various valves and instantaneous and precise measurements of pistonpositions with robotic speed significantly reduces the time operatorsregularly spend on routine operations. For instance, a forklift can beprogrammed for the appropriate height corresponding to a shipping dockif computer control is implemented.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 shows a Double-Acting Cylinder With Hinge Mount.

FIG. 2—shows a Transmission Line with a Short Termination.

FIG. 3 shows Phase Angle of Reflection Coefficient ∠Γ versus Frequencyfor a shorted Transmission line

FIG. 4 shows the Slope of Phase Angle vs. Frequency at different Pistondepths

FIG. 5 shows a Typical System Configuration of the invention showingrespectively two views from two different sides.

FIG. 6 shows a Typical System Diagram For measuring |Γ| and φ withmultiple down conversion.

FIG. 7 shows a Typical System Diagram For Measuring |Γ| and φ′.

FIG. 8 shows a Typical System Diagram Using Amplitude ModulationTechnique

FIG. 9 shows a Typical Amplitude And Phase of Reflection Coefficient inhydraulic cylinder

FIG. 10 shows a Field configurations, first is TE^(Z) and/or TM^(Z)modes in a circular waveguide

FIG. 11 shows a Field configurations, additional 15 TE^(Z) and/or TM^(Z)modes in a circular waveguide

FIG. 12 a shows a Solid Antenna For TM01 Mode

FIG. 12 b shows a Wire Mesh Antenna For TM01 Mode

FIG. 13 a shows a Antenna For TM02 Mode

FIG. 13 b shows the Antenna For TM03 Mode

FIG. 14 shows the Field Configurations for TE^(Z) modes in a coaxialwaveguide

FIG. 15 a shows the Field configurations for TM^(Z) modes in a coaxialwaveguide

FIG. 15 b shows the Field configurations for TM^(Z) modes in a circularwave-guide

FIG. 16 shows a End-Fed Antenna

FIG. 17 shows a Side Fed Antenna

FIG. 18 shows an End Fed Antenna Implementation For TM₁₁, Mode

FIG. 19 shows a Cylinder with Temperature and Pressure Sensors

FIG. 20 shows a Cylinder with sensor for measuring relative dielectricconstant ε_(r) and ε_(r)′ (loss tangent)

FIG. 21 shows a Side-Fed Antenna

FIG. 22 shows a Typical System Diagram One-Port Network Analyzer

FIG. 23 shows a Typical cylinder head with an antenna installed in it.

FIG. 24 shows a Typical antenna structure for antenna installed in theend cap which contains the piston arm.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

I. Theory of Operation

A detailed description of the theoretical concepts for the analysis andapplications of hydraulic systems and their components such as hydraulicpistons, cylinders, pumps and control valves is discussed in ref [1].FIG. 1 depicts a typical double-acting cylinder with a hinge. As FIG. 1depicts, one side-is a hollow cylinder (blind end) filled with hydraulicfluid (oil) or pneumatic fluid (air). The other side contains a pistonarm (rod). The space between the piston arm and the cylinder wall isfilled with the same hydraulic fluid. In order to move the arm(s), thehydraulic fluid enters one side and the fluid exits from the other side.The hollow side can be viewed as a uniform cylindrical waveguide withcircular cross section.

To estimate the piston's position, waveguide and transmission linetheories are utilized. The cylinder functions as a waveguide and thepiston functions as an electrical short. The position of the piston inthe hydraulic/pneumatic cylinder is determined using the phase of thevoltage reflection coefficient versus frequency. Usually, the slope ofthe voltage reflection coefficient is used. Instead the rate of changeof the phase with respect to frequency, the total phase shift in a givenfrequency range is used.

In a uniform cylindrical waveguide with circular cross section, theguide wavelength depends on the dimensions of the waveguide and thecomposition of the material that fills the waveguide; this is given bythe following equation

$\begin{matrix}{\lambda_{z,{mn}} = \frac{\lambda}{\sqrt{1 - \left( {f_{c,{mn}}/f} \right)^{2}}}} & (1)\end{matrix}$where

-   -   λ_(z,mn)=wavelength in the longitudinal or guide direction of        the        -   mn-th waveguide mode of propagation (assumed here to be the            z-direction)    -   m,n=indices identifying the various waveguide modes

$\lambda = {{\frac{c}{f}\frac{1}{\sqrt{ɛ_{r}\mu_{r}}}} = {{intrinsic}\mspace{14mu}{wavelength}\mspace{14mu}{of}\mspace{14mu}{the}\mspace{14mu}{medium}\mspace{14mu}{filling}\mspace{14mu}{the}\mspace{14mu}{waveguide}}}$

-   -   ƒ_(c,mn)=cutoff frequency of the mn-th waveguide mode which        depends on the        -   dimensions of the waveguide and the electrical parameters μ            and ε of the medium filling the waveguide.    -   ƒ=frequency of the wave

μ=permeability of the material that fills the Wa1veguide

-   -   ε=permittivity of the material that fills the waveguide

For convenience, (1) is re-written as

$\begin{matrix}{\lambda_{z,{mn}} = \frac{c}{f\sqrt{ɛ_{r}\mu_{r}}\sqrt{1 - \left( \frac{f_{c,{mn}}}{f} \right)^{2}}}} & (2)\end{matrix}$where

-   -   ε_(r)=relative permittivity    -   μ_(r)=relative permeability which equals unity for non-magnetic        material

FIG. 2 depicts a standard lossless transmission line. The total phaseshift of the voltage reflection coefficient the shorted transmissionline of length d is given by

$\begin{matrix}{{{\angle\Gamma} = {{\phi_{r}\left( {d,f} \right)} = {\pi - {2\beta_{z}d}}}}{where}} & (3) \\{\beta_{z,{mn}} = \frac{2\pi}{\lambda_{z,{mn}}}} & \left( {3a} \right)\end{matrix}$

-   -   β_(Z) is the guide (z-direction)phase constant of the waveguide        mode, which by Substituting (3 a) into (3) yield

$\begin{matrix}{{\phi_{r}\left( {d,f} \right)} = {{\pi - \frac{4\pi\; d}{\lambda_{z,{mn}}}} = {\pi - \frac{4\pi\;{fd}}{v_{{pz},{mn}}}}}} & (4)\end{matrix}$where

-   -   ν_(pz,mn)=Phase velocity in the guide for the mn-th waveguide        mode of propagation (assumed here to be the z-direction) or

$\begin{matrix}{d = {{\frac{\lambda_{z,{mn}}}{4\pi}\left\lbrack {\pi - {\phi_{r}\left( {d,f} \right)}} \right\rbrack} = {\frac{v_{p,{mn}}}{4\pi\; f}\left\lbrack {\pi - {\phi_{r}\left( {d,f} \right)}} \right\rbrack}}} & (5)\end{matrix}$

In order to obtain the length of a shorted transmission line d using(5), the measured phase shift {circumflex over (φ)}_(r)(d,ƒ) in generalis insufficient since the instrumentation can only measure phase shiftsin the range of [−π,+π]and for phase shifts that are more than +π singlefrequency phase shift measurement has an ambiguity of +2kπ for k=. ..−3,−2,−1,0,+1,+2,+3, . . . . In order to resolve the ambiguityresulting from the limitation of range of [−π,+π] in the availablemeasurement techniques, one could alternatively measure the slope of thephase shift with respect to frequency i.e.,

$\frac{\partial{{\hat{\phi}}_{r}\left( {d,f} \right)}}{\partial f}$which equals

${\frac{\partial{\phi_{r}\left( {d,f} \right)}}{\partial f}\mspace{14mu}{or}},$alternatively, measure a sweep of phase shifts with respect tofrequency.

FIG. 3 is a plot of frequency sweep of the phase angle of the voltagereflection coefficient φ_(r)(d,ƒ) for a shorted transmission line.

Another approach for the determination of the length d of the shortedtransmission line is accomplished by using the phase slope of thereflection coefficient with respect to frequency. By taking partialderivative with respect to frequency on both sides of (4) we obtain

$\begin{matrix}{\frac{\partial{\phi_{r}\left( {d,f} \right)}}{\partial f} = {{- 4}\pi\; d\frac{\partial\left( \frac{f}{v_{p,{mn}}} \right)}{\partial f}}} & (6)\end{matrix}$

In a hollow waveguides filled with dielectric material, the phasevelocity for the mn-th waveguide mode of propagation (assumed here to bethe z-direction) is given by¹ν_(pz,mn)=λ_(z,mn)·ƒ  (7)A detailed description of the theoretical concepts for the analysis ofthe fields in cylindrical waveguides may be found in ref [2].where

ν_(pz,mn)=phase velocity in the waveguide associated with modes m

-   -   and n

Using (2) in (7) yields

$\begin{matrix}{{v_{{pz},{mn}}(f)} = \frac{c}{\sqrt{ɛ_{r}\mu_{r}}\sqrt{1 - \left( \frac{f_{c,{mn}}}{f} \right)^{2}}}} & (8)\end{matrix}$where the cutoff frequency f_(c) for circular waveguide is given by

$\begin{matrix}{f_{c,{mn}} = \frac{\chi_{mn}^{\prime}}{2\pi\; a\sqrt{\mu ɛ}}} & (9) \\{f_{c,{mn}} = \frac{\chi_{mn}}{2\pi\; a\sqrt{\mu ɛ}}} & (10)\end{matrix}$

with

χ′_(mn)=n-th zero (n=1, 2, 3, . . . ) of the derivative of

-   -   the Bessel function J_(m) of the first kind of order (m=0, 1, 2,        3, . . . ) which is used for TE modes. Values corresponding to        various indices of χ′_(mn)are provided in page 472 of reference        [2].    -   χ_(mn)=the n-th zero (n=1, 2, 3, . . . ) of the Bessel        -   function J_(m) of the first kind of order (m=0, 1, 2, 3, . .            . ) which is used for TM modes.            Values corresponding to various indices of χ_(mn) are            provided on page 478 of the reference [2].            substituting (8) into (6) one can obtain

$\begin{matrix}{\frac{{\partial\phi_{r}}\;\left( {d,f} \right)}{\partial f} = {\phi_{r}^{\prime} = {{{- \frac{4\;\pi\; d\;\sqrt{ɛ_{r}\;\mu_{r}}}{c}}\;\frac{\partial\left( {f\;\sqrt{1 - \left( \frac{f_{c}}{f} \right)^{2}}} \right)}{\partial f}} = {{- \frac{4\;\pi\; d\;\sqrt{ɛ_{r}\;\mu_{r}}}{c}}\;\left( {\sqrt{1 - \left( \frac{f_{c}}{f} \right)^{2}} + \frac{f_{c}^{2}}{f^{2}\;\sqrt{1 - \left( \frac{f_{c}}{f} \right)^{2}}}} \right)}}}} & (11) \\{{From}\mspace{14mu}(11)} & \; \\{d = {{- \frac{\phi_{r}^{\prime} \cdot c}{4\;\pi}} \cdot \sqrt{\frac{1}{\mu ɛ}} \cdot \frac{1}{\sqrt{1 - \left( \frac{f_{c}}{f} \right)^{2}}\; + \frac{f_{c}^{2}}{f^{2}\;\sqrt{1 - \left( \frac{f_{c}}{f} \right)^{2}}}}}} & (12) \\{d = {\frac{t_{gd}c}{2} \cdot \sqrt{\frac{1}{\mu ɛ}} \cdot \frac{1}{\sqrt{1 - \left( \frac{f_{c}}{f} \right)^{2}} + \frac{f_{c}^{2}}{f^{2}\sqrt{1 - \left( \frac{f_{c}}{f} \right)^{2}}}}}} & (13)\end{matrix}$where t_(gd) is the group delay given by

$\begin{matrix}{{t_{gd} \equiv {- \frac{\partial\phi_{r}}{\partial\omega}}} = {- \frac{\partial\phi_{r}}{2\pi{\partial f}}}} & (14)\end{matrix}$In an alternative methodology, a phase sweep in the frequency range of[ƒ₁,ƒ₂] can be used. Using (4)

$\begin{matrix}{{{{\phi_{r}\left( {d,f_{2}} \right)} - {\phi_{r}\left( {d,f_{1}} \right)}} = {\frac{4\pi\; f_{1}d}{v_{{pz},{mn}}\left( f_{1} \right)} - \frac{4\pi\; f_{2}d}{v_{{pz},{mn}}\left( f_{2} \right)}}}{or}} & (15) \\{d = \frac{{\phi_{r}\left( {d,f_{2}} \right)} - {\phi_{r}\left( {d,f_{1}} \right)}}{\frac{4\pi\; f_{1}}{v_{{pz},{mn}}\left( f_{1} \right)} - \frac{4\pi\; f_{2}}{v_{{pz},{mn}}\left( f_{2} \right)}}} & (16)\end{matrix}$FIG. 4 depicts typical curves for the slope of the phase angle of thevoltage reflection coefficient φ′_(r) versus frequency ƒ. Once a valuefor the slope of the phase angle φ′_(r) or time delay t_(gd) isdetermined, the piston distance d can be determined from (14) or (15) orutilizing curves such as those in FIG. 4 or by a table-lookup.Implementation FIGS. 10, 11, and 15 b depict the field lines of lowerorder modes in the cross section of a hollow cylindrical waveguide;these correspond to the hollow side of hydraulic/pneumatic cylinder.

FIGS. 14, 15 a depict field lines of the lower order modes of a coaxialwaveguide; these correspond to the side of cylinder hydraulic/pneumaticcontaining the piston arm. Either side can be used as the waveguideregion. However, due to presence of less available space in chamberwhich contains the piston arm the hollow side is usually preferable forplacing an antenna.

As shown in FIG. 5 the antenna 150 is placed at the blind end ofmetallic cylindrical chamber. According to this embodiment the feednetwork 152 connects via radio frequency connector 166 and cable 154 andradio frequency connector 162 through coaxial section 162 to the antenna150. According to this figure the cable 154 passes through the spacebetween the hinges 158 and 160 of the blind end cap and connects toradio frequency connector 162. As the piston 165 and the piston arm 156moves the distance d which is the distance between the antenna 150 andpiston 160 changes. The feed network 152 is typically a one port networkanalyzer. FIGS. 6, 7, 8 and 22 are typical implementation of such oneport network analyzer systems. The network analyzer determines theelectrical length of the cylinder between the antenna 150 and piston165. The electrical length of the cylinder, i.e., the electricaldistance from a reference point at the antenna 150 to the piston 165 isdetermined by using the measured phase versus frequency information asdescribed above. The electrical lengths of the connecting cable 154 andradio frequency connectors 158 and 164 are known and are subtracted fromthe actual measurements. The cutoff frequency ƒ_(c) is calculated by (9)or (10) by inputting values for the inner radius β of the cylinder andthe relative permittivity ε_(r), and permeability μ_(r) of the fluidfilling the cylinder. The piston depth d is calculated from any ofequations (12), (13) or (16).

Alternatively, the antenna can be installed on the arm end utilizingcoaxial waveguide modes. In that case the field lines have to match thefield lines of FIGS. 14 and 15. For example for E₁₁ mode as in FIG. 15 aan antenna implementation is composed of two rods located at the nodesof field lines. FIG. 23.

The antenna is connected to circuitry that measures the voltagereflection coefficient Γ (both in magnitude and phase). The phase slopewith respect to frequency, is calculated and is proportional to thegroup delay. The phase non-linearity causes uncertainty in themeasurements. The non-linearity data (shown in FIG. 4) is obtained whenthe piston is at a known distance d, (e.g., when the arm is extended allthe way out). At these same points, the phase slope measurementsφ′_(r)(d,ƒ) are also obtained and stored in computer memory by thesoftware.

FIGS. 6, 7, 8 and 22 depict the block diagrams for variousimplementations of one port network measurements. Both the phase angleand the magnitude of voltage reflection coefficient are measured. Themagnitude of the reflection coefficient (return loss) |Γ| predicts theloss tangent ∈″ of the hydraulic fluid. By incorporating the losstangent in the formulation i.e. substituting ∈_(r)=∈′−j∈″ the aboveequations more measurement accuracy is obtained.

FIGS. 6, 7, 8 and 22 depict four possible methods (amongst a variety ofpossible techniques) for the measurement of the magnitude, phase angleand its derivative with respect to frequency, i.e., the phase slopeφ′_(r)(d,f) or the group delay t_(gd) of the voltage reflectioncoefficient for different piston depths at different frequencies. InFIG. 8 the phase slope or equivalently the group delay is measureddirectly by means of amplitude modulation techniques. The high frequencycarrier signal that is amplitude modulated by a low frequency“base-band” signal and the delay in the base-band incurred as a resultof passing through the cylinder under the test is measured.

As in FIGS. 6, 7, 8 and 22 indicated, the signal from the sourcecircuitry 210, 210 a [such as a phase-locked loop (PLL) or directdigital synthesis (DDS) device or combination of both] is coupled to aport of a three port directional device 209 such as a bridge e.g., adirectional coupler or a circulator. The other port is connected to theantenna mounted in the cylinder. The signal is coupled into the cylinderand reflected by the piston. The reflected signal is coupled back to thedevice and is coupled to its third port. By utilizing such directionalthree-port devices 209, the reflected wave from the cylinder-piston isseparated from the incident wave. The phase of the reflected signal iscompared to the phase of the incident signal either at the radiofrequency or a lower frequency using a phase comparator 214 in order toobtain the phase angle of the voltage reflection coefficient,φ_(r)(d,ƒ). The ratio of the amplitude of the reflected signal to theamplitude of the incident reference (signal source) yields the magnitudeof voltage. When the measurements are repeated for differentfrequencies, the piston location is determined using (12), (13) or (16).The frequency selection is controlled by micro-controller 213. Inanother system configuration such as FIG. 7 the micro-controller 215handles the calculation of phase slope from the measured phase inaddition to controlling the frequency of the source. According toanother embodiment as described in FIG. 8 the phase slope orequivalently the group delay can be calculated utilizing amplitudemodulation. A low frequency signal source 218 provides the basebandsignal to a carrier frequency generated by microwave signal source 210using amplitude modulator 219. The modulated signal is then split intotwo separate signals by power splitter 211. One branch of the splitsignal feeds the AM detector 216 a and detects the baseband signal whichin turn feeds on input of phase comparator 214. The other branch of thesplit signal from power splitter 211 feeds the first port of directionaldevice 209. The signal from the second port of the directional device209 via connectors and cable couples a signal to the antenna in thecylinder. The reflected signal from the couples back from the cylinderto the second port of directional device 209 and in turn the signal iscoupled out from the third port of directional device 209 to AM detector216 b which feed the input port of the phase comparator 214. The phasecomparator then provides the phase difference and or the group delay.The AM detector 216 feeds a secondary AM detector 217 in order to obtainthe magnitude of the reflection coefficient. In another implementationaccording to FIG. 22, microprocessor 226 controls the frequency ofsignal source 210 which feeds the power splitter 211. One port of thepower splitter 211 feeds port one of a directional device 229 and thenthe signal from its second port is coupled to cylinder and thenreflected back by the piston in turn coupled back to the second port ofdirectional device 229 and then coupled out from the third port ofdirectional device 229 feeding an attenuator 228 and in turn feeding theRF ports of two frequency mixers which operate as phase detectors. Theother port of power splitter 211 feeds a quadrature device whichprovides a 90° phase shift between its outputs feeding the LO ports ofthe of two frequency mixers. The IF ports of the of two frequency mixersprovides the I and Q channels of the reflection coefficient Γ in turnare digitized via analog to digital converters 215 a,b which in turnfeeding a digital signal processor or micro-processor 226. Themicro-processor calculates the phase difference and subsequentlycalculates the distance according to one of the formulations mentionedabove and outputs the measured distance d.

Antenna Implementation

Typically antenna design is implemented by use of a rod serving as thecenter conductor of a quarter wave coaxial transformer matching theinput impedance (typically 50 Ω) to the wave impedance of the waveguide.Since the wave impedance of the hollow portion of the waveguide isknown, the wave impedance of the coaxial portion is determined.

Non-Idealistic Behavior of System Components Ideal transmission linesexhibit a constant delay versus frequency and thereby results in alinear phase versus frequency characteristic. However, waveguidesdeviate from ideal transmission lines and have dispersivecharacteristics with respect to frequency as is evident by the phasevelocities being frequency dependent; (5). Other effects such asmismatches in various components of the system, e.g., the antenna,connectors and parasitic capacitances, result in additional phasenon-linearities. The piston is not a perfect short due to the fact thatit has recessed rings acting as capacitors. The lossy nature of thehydraulic fluid causes additional dispersion. In addition, thenon-linear effects due to the presence of antenna evanescent modes aremore significant when the piston is close to the antenna. Due to thenon-zero loss tangent of the hydraulic fluid and the finite conductivityof the metallic portions of the system, the magnitude of the reflectioncoefficient is less than unity. Hence, the phase versus frequencycharacteristics are not linear. FIG. 9 depicts typical phase andamplitude versus frequency characteristics of the voltage reflectioncoefficient for a typical hydraulic cylinder.Antenna Mode of Operation

FIGS. 10 and 11 depict the cross-sectional field configuration of thefirst 30 TE^(Z) and/or TM^(Z) modes of a uniform cylindrical waveguideincorporated in here from reference [2]. A preferred implementation ofthe apparatus for hydraulic cylinder depth measurement occurs whenplacing the antenna in the hollow side of the cylinder and utilizing theTM₀₁ mode of a circular waveguide. This modal selection is due to thesimilarity of the field lines of the TM₀₁ mode in a hollow cylindricalwaveguide to the field lines of a coaxial transmission lines. Theelectric field lines are radial and the magnetic field lines arecomposed of concentric circles; there are no nulls in the fielddistributions along the radius. FIGS. 12-a and 12-b depict the novelgeometrical construction of the antenna choice to produce the neededTM₀₁ modes. In FIG. 12-a, the antenna is implemented using solid metal.The far right portion of the antenna is tapered. The tapered shapeprovides a radial component of the electric field only at the center tobe zero as the field configuration for TM₀₁ mode (FIG. 10). This is donein order to minimize excitation of waveguide evanescent modes whichtheir presence at the close proximity of the antenna would interferewhen the piston gets close to the antenna. In FIG. 12-b, the rigid wiresforming a mesh structure are utilized for the construction of theantenna. This type of antenna produces more evanescent mode fields sinceit does not have the tapered tip. Other modes of operation can beimplemented by antennas made of multiple conductors.

FIG. 13 a depicts the views of the cross sections of the side and thefront of an antenna for generating TM02 mode which corresponds to thefield configuration for the TM02 as depicted in FIG. 10. The innerconductor 234 is separated from the outer conductor 230 via insulator231. The conductors 230 and 231 are fed with a feed network.

FIG. 13 b depicts the views of the cross sections of the side and thefront of an antenna for generating TM03 mode which corresponds to thefield configuration for the TM03 as depicted in FIG. 11 The innerconductor 230 is separated from the intermediate conductor 236 viainsulator 239 and the outer conductor 237 is separated from intermediateconductor 236 via the insulator 238. The conductors 235 and 236 and 237are fed with a feed network.

FIG. 14 shows the Field Configurations for TE^(Z) modes in a coaxialwaveguide brought here from ref [3]. FIG. 15 a shows the Fieldconfigurations for TM^(Z) modes in a coaxial waveguide brought here fromref [3]. FIG. 15 b shows the Field configurations for TM^(Z) modes in acircular wave-guide brought here from ref [3]

FIG. 16 shows a End-Fed Antenna. This type of implementation isappropriate for the type of cylinders which have two flanges on the endcap and the connector 206 is attached to the cylinder 111 and feeds theantenna 204 from the space between the hinges. The antenna 204 isseparated from the cylinder 11 via insulator 208.

FIG. 17 shows a Side Fed Antenna. This type of implementation isappropriate for the type of cylinders which have one flange on the endcap 112 which is at the center of the end cap and the preferableapproach is to attach and the connector 206 to the cylinder 111 and fromthe side which feeds the antenna 204 from the space away from the hinge.The antenna 204 is separated from the cylinder 11 via insulator 208

FIG. 18 shows an End Fed Antenna Implementation For TM₁₁ Mode of twoseparate antennas 204 which consists

FIG. 19 shows a Cylinder 111 with Temperature sensor 220 and Pressuresensor 221 Sensors installed on the cylinder. The temperature andpressure change the electrical properties of the hydraulic/pneumaticfluid 102. The data for relative permitivitty ∈_(r)=∈′−j∈″ versuspressure and temperature is the table and as necessary is looked up bythe computer/digital processor in order to maintain the accuracy of themeasurements as pressure and temperature changes due to factors such asfriction load and the surrounding environments.

Alternatively, as in FIG. 20 the cylinder 101 is equipped with sensorfor measuring relative dielectric constant ∈_(r)=∈′−j∈″ of the fluid 102directly. This type of sensor could be implemented by using a capacitorin which the fluid penetrates between its plates.

FIG. 21 depicts another Side-Fed Antenna configuration in which theradiating portion of the antenna 223 is mounted on an insulator 208 acoaxial line feeds the signal from connector 206 to the antenna 223 viaflexible contact 208. One possible method of securing the insulator 208to the cylinder 101 is by cutting annular notches in the cylinder 101and insulator 208. A spring washer 114 is inserted in the annular notchof the insulator 208. Spring 115 is placed on the bottom of cylinder101. The washer 114 is squeezed and the insulator is inserted in thecylinder and as the washer 114 reaches the notch in the cylinder 101 itexpands and secures the insulator 208 in place.

FIG. 23 depicts an actual antenna with tapered end installed in an endcap.

FIG. 24 depicts a typical structure of antenna installed in the end cap251 when a piston arm 254 is present. The signal is provided to the tworadiators 252 and 253 by means of a feed network 256. The radiators 253and 254 are separated from the end cap 251 by insulators 258. The feednetwork 256 functions as a two way power splitter and its outputs isconnected to the antennas via cables 260 and 261 and connectors 262 and263 flexible connecting rods 264 and 265. This arrangement produces TM₁₁mode which is referred to E₁₁ in reference [3] as its fieldconfiguration are depicted in FIG. 15 a. As seen in FIG. 15 a the fieldconfiguration for E₁₁, has two nodes corresponding to the tips ofradiators 253 and 254. The antenna system as described in FIG. 24produces field configuration E₁₁ as in FIG. 15 a. However, in order toobtain higher order modes more number radiators is necessary for exampleby using four radiators produces four nodes corresponding to E₂₁ mode,i.e., as field configuration E₂₁ as in FIG. 15 a. the advantage ofhigher order modes is the radiator rods are shorter and would not takeas much space. Cylinders with double end rod construction require suchantenna due to the fact that both ends contain a piston arm. However, inany event such antenna system can be utilized in a in a single end rodcylinders in the rod side.

Calibration

In order to improve the measurement accuracy a calibration procedure forreducing the unwanted characteristics of the antenna as well as theother components of the system is performed. The one port networkanalyzer also goes through a calibration procedure with short, open andtermination as done in lab equipment In on method the data collecteddata versus actual measurements are saved in a table and is used astable took up for interpolation. In another method the effectsmeasurements of the antenna characteristics and the other RF componentsare calibrated out of the measurements.

REFERENCE

-   [1] Charles S. Hedges, Industrial Fluid Power Volume 1, Third    Edition (1984).-   [2] C. A. Balanis, Advanced Engineering Electromagnetics, pp.    470-491 (1989)-   [3] Nathan Marcuvitz, Waveguide Handbook (1986)

1. A system for measurement of piston displacement in a fluid filledcylinder, said system comprising: an antenna, disposed at one end ofsaid cylinder; and a signal source configured to generate an electronicsignal which is coupled to the cylinder such that said signal reflectedoff of said piston is measured at said antenna, such that the distancesaid piston is from said antenna is measured by using one or both ofmeasurement signals including the relationship between a slope of thephase angle of the reflection coefficient and the frequency or groupdelay associated with the reflection coefficient.
 2. The system asclaimed in claim 1, wherein said antenna is a solid antennasubstantially generating TM01 Mode.
 3. The system as claimed in claim 1,wherein said antenna is a mesh antenna substantially generating TM01Mode.
 4. The system as claimed in claim 1, wherein said antenna is anantenna substantially generating TM02 Mode.
 5. The system as claimed inclaim 1, wherein said antenna is an antenna substantially generatingTM03 Mode.
 6. The system as claimed in claim 1, wherein said antenna isan end fed antenna which signal is being launched from end cap piece. 7.The system as claimed in claim 1, wherein said antenna is a side fedantenna which signal is being launched from the side of an end cappiece.
 8. The system as claimed in claim 1, wherein said antenna is anantenna substantially generating TM11 Mode.
 9. The system as claimed inclaim 1, wherein the dielectric constant and loss tangent of the fluidfilling the cylinder is determined by a calibration process in which thepiston is moved to the extreme(s).
 10. The system as claimed in claim 1,further comprising a temperature sensor that is used to estimate thechanges in dielectric constant and loss tangent of the fluid filling thecylinder.
 11. The system as claimed in claim 1, further comprising apressure sensor that is used to estimate the changes in characteristicsof the fluid filling the cylinder due to pressure changes.
 12. Thesystem as claimed in claim 1, further comprising a temperature sensorthat is used to estimate changes in characteristics of the fluid fillingthe cylinder due to temperature changes.
 13. The system as claimed inclaim 1, further comprising a One-Port Network Analyzer for measuringthe piston displacement.
 14. The system as claimed in claim 1, whereinsaid antenna is installed in an end cap that contains an arm of saidpiston.
 15. The system as claimed in claim 14, wherein said antennautilizes coaxial waveguide modes.
 16. The system as claimed in claim 15wherein the antenna implementation is composed of two rods located atnodes of field lines.
 17. The system as claimed in claim 1, wherein boththe phase angle and the magnitude of voltage reflection coefficient aremeasured in order to determine both the dielectric constant and the losstangent of hydraulic fluid in said piston and incorporating both theloss tangent and the dielectric constant in a formulation for obtainingmeasurement accuracy.
 18. The system as claimed in claim 1, whereingroup delay is measured directly by means of amplitude modulationtechniques.
 19. The system as claimed in claim 1, wherein a phase-lockedloop (PLL) or direct digital synthesis (DDS) device or combination ofboth is utilized for said signal source.
 20. The system as claimed inclaim 1, further comprising a directional coupler or a circulatorutilized to separate the transmit and receive signals.
 21. The system asclaimed in claim 1, wherein said antenna is a rod serving as the centerconductor of a quarter wave coaxial transformer matching the inputimpedance to the wave impedance of a waveguide.
 22. The system asclaimed in claim 1, wherein said antenna is installed in a hollow sideof said cylinder and utilizes the TM01 mode of a circular waveguide. 23.The system for the measurement of piston displacement in a fluid filledcylinder as claimed in claim 1, wherein said antenna has a tapered endshape providing substantially no excitation evanescent modes in anoperation mode.
 24. The system as claimed in claim 1, wherein saidantenna employs a multiple conductor mode of operation.
 25. The systemas claimed in claim 1, wherein said antenna is supported by an insulatorcontaining annular notches.
 26. The system as claimed in claim 1,wherein said antenna includes distinct conductors and a feed network.27. The system as claimed in claim 1, wherein data collected versusactual measurements are saved in a table and are used as table look upfor interpolation.
 28. The system as claimed in claim 1, wherein theeffects from non-idealistic characteristics of at least some componentsof said system are accounted for by a calibration procedure.